We study an even order system boundary value problem with
periodic boundary conditions. By establishing
the existence of a positive eigenvalue of an associated linear system
Sturm-Liouville problem, we obtain new conditions for the boundary
value problem to have a positive solution. Our major tools are the
Krein-Rutman theorem for linear spectra and the fixed point index theory
for compact operators.

The well-known Falkner--Skan equation is one of the most important
equations in laminar boundary layer theory and is used to describe
the steady two-dimensional flow of a slightly viscous
incompressible fluid past wedge shaped bodies of angles related to
$\lambda\pi/2$, where $\lambda\in \mathbb R$ is a parameter
involved in the equation. It is known that there exists
$\lambda^{*}<0$ such that the equation with suitable boundary
conditions has at least one positive solution for each $\lambda\ge
\lambda^{*}$ and has no positive solutions for
$\lambda
Keywords:Falkner-Skan equation, boundary layer problems, singular integral equation, positive solutionsCategories:34B16, 34B18, 34B40, 76D10